Morse Matchings on a Hypersimplex

We present a family of complete acyclic Morse matchings on the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. In a future paper we will utilize these matchings to classify every subcomplex whose reduced homology groups are concentrated in a single degree and describe a homology basis for each of them.Comment: part of phD thesis arXiv:1108.6001. arXiv admin note: text overlap with arXiv:0806.1503 by other author

Homology Representations Arising from a Hypersimplex

We present a complete acyclic matching of the Hasse diagram associated with the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. We will then utilize this matching along with discrete Morse theory and some topological techniques to classify every subcomplex whose reduced homology groups are concentrated in a single degree. These reduced homology groups support a natural action of the symmetric group and a description of the characters that this action produces is given

Brief Consultation to Families of Treatment Refusers with Symptoms of Obsessive Compulsive Disorder: Does It Impact Family Accommodation and Quality of Life?

Family members are often directly and significantly impacted by the restrictive demands of OCD, a frequently disabling disorder. Family accommodation behaviors (i.e., doing things for or because of the OCD sufferer that a person would not normally do) are associated with dysfunction, including poorer treatment responses in OCD sufferers and greater distress in family members. Although evidence suggests family-based intervention can reduce symptoms in OCD sufferers who participate in treatment, there is a lack of research documenting the impact of interventions designed for the families of OCD treatment refusers (TR). Brief Family Consultation (BFC) was developed by our clinical team to help families refocus their efforts on the things that they can realistically control and change (e.g., participation in compulsions). In this crossover study, twenty families related to an individual who exhibited OCD symptoms but had refused treatment were assigned to five phone sessions of either BFC or a psychoeducation condition. Compared to this credible, attention-placebo control group (Brief Educational Support; BES), BFC (but not BES) resulted in reductions in family accommodation behavior, yet neither BFC nor BES resulted in improved quality of life for family members of treatment refusers. BFC is one of the first interventions to be evaluated for its ability to help families when their loved ones with obsessive compulsive symptoms refuse treatment. This pilot study provides new insights for clinicians and researchers to better address the needs of these neglected families

Morse matchings on polytopes

We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cube polytope studied in previous works. This involves constructing explicit complete acyclic Morse matchings on the face lattice of the half cube; this procedure may be of independent interest for other highly symmetric polytopes